A127669 Number of numbers mapped to A127668(n) with the map described there.

1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 5, 1, 3, 1, 3, 2, 2, 1, 5, 2, 2, 3, 3, 1, 3, 2, 7, 2, 2, 2, 5, 1, 2, 2, 5, 1, 3, 1, 3, 3, 2, 1, 7, 2, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 5, 1, 3, 3, 11, 2, 3, 1, 3, 2, 3, 1, 7, 2, 2, 3, 3, 2, 3, 2, 7, 5, 2, 1, 5, 2, 2, 2, 5, 1, 5, 2, 3, 2, 2, 2, 11, 1, 3, 3, 5

Offset

2,3

Comments

This is not A008481(n), n>=2, which starts similarly, but differs, beginning with n=24.

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Formula

a(n) <= pa(Length( A127668(n))), n>=2. Length gives the number of digits and pa(k):=A000041(k) (partition numbers). (It was originally claimed that this is equality, but that is not correct. - Franklin T. Adams-Watters, May 21 2014)

Example

a(4)=2 because two numbers are mapped to 11= A127668(4), namely n=p(1)*p(1)=4 and n=p(11)=31. p(n)=A000041(n) (partition numbers).
a(24)=5 but A008481(24)=4.
The five numbers mapped to A127668(24)= 2111 are: 18433, 2594, 2263, 292, 24.

Maple

f:= proc(n) local S;
   nops(g(sprintf("%d", n)))
end proc:
g:= proc(s) option remember;
    local S, m, k1;
    if s[1] = "0" then return {} fi;
    S:= {[parse(s)]};
    for m from 1 to length(s)-1 do
      k1:= parse(s[1..m]);
      S:= S union map(t -> [k1, op(t)], select(r -> r[1] <= k1, procname(s[m+1..-1])));
    od;
    S;
end proc:
h:= proc(n) local F;
  F:= map(t -> numtheory:-pi(t[1])$t[2], sort(ifactors(n)[2], (a, b) -> a[1] > b[1]));
  parse(cat(op(F)))
end proc:
seq(f(h(i)), i=2..100); # Robert Israel, Dec 08 2024

Crossrefs

Cf. A008481, A127668.

Sequence in context: A329617 A008481 A318473 * A323436 A056692 A331600

Adjacent sequences: A127666 A127667 A127668 * A127670 A127671 A127672

Keyword

nonn,easy,base

Author

Wolfdieter Lang Jan 23 2007

Extensions

Edited by Franklin T. Adams-Watters, May 21 2014

Corrected by Robert Israel, Dec 08 2024

Status

approved